Preheat the oven to 350F (175C).

Line 10 muffin cups with paper liners.

In a large bowl, whisk together coconut flour, arrowroot powder, baking soda, cinnamon, and nutmeg.

In a medium bowl, whisk together the eggs, grapeseed oil, and agave nectar.

Pour the wet ingredients into the dry ingredients.

Using a handheld mixer, blend until thoroughly combined.

Gently fold in the coarsely chopped green apple.

Scoop 1/4 cup of batter into each prepared muffin cup.

Bake for 18 to 23 minutes.

Check for doneness by inserting a toothpick into the center of a cupcake.

If the toothpick comes out with just a few moist crumbs, the cupcakes are ready.

Remove the cupcakes from the oven and let them cool in the pan for 1 hour.

Frost and serve the cupcakes.